# amplifier with 2 capacitors

#### mzsyed85

Joined Jan 1, 2009
10
Hey guys,
I am having some problems making the correct assumptions involving an inverting amplifier (attached)...
Assumptions:
I1 = I2
V- = 0

I1 = C1 (dVin/dt)
I2 = C2 (-dVout/dt)

Question: Prove Vout = -Vin(C1/C2)

I have arrived at this solution, but I am not sure I did it the right way or I got my assumptions right by coincidence - specifically for I2. Even then, I may have jumped a step which seems a bit dodgy to me now...

Since I1 = I2,

C1(dVin/dt) = C2(-dVout/dt)
C1(dVin) = C2(-dVout)
dVout = -dVin(C1/C2)

therefore Vout = -Vin(C1/C2)

Could somebody tell me whether I did this correctly? For some reason I feel I am not allowed to get rid of the 'd' that easily...
Thank you

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#### mik3

Joined Feb 4, 2008
4,846
To remove the 'd' you have to integrate both sides of your equation

dVout = -dVin(C1/C2)

integral of dVout=Vout

integral of dVin=Vin

and thus

Vout=-Vin(C1/C2)

#### Wendy

Joined Mar 24, 2008
21,840
Of course, in the real world the op amp would promptly saturate on one or the other power supply rail. Interesting concept though, I don't think they ever hit us with that one in school.

#### mik3

Joined Feb 4, 2008
4,846
You are right Bill,this is the problem with schools and universities, they don't explain to the students what practical problems arise from the circuits.